scholarly journals Simulation of Ruin Probabilities for Subexponential Claims

1997 ◽  
Vol 27 (2) ◽  
pp. 297-318 ◽  
Author(s):  
S. Asmussen ◽  
K. Binswanger
Keyword(s):  
Ruin Probability ◽  
Asymptotic Efficiency ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Simulation Methods ◽  
Classical Risk Model ◽  
Claim Size Distribution ◽  
Conditional Monte Carlo ◽  
Asymptotically Efficient ◽  
The Classical Risk Model

AbstractWe consider the classical risk model with subexponential claim size distribution. Three methods are presented to simulate the probability of ultimate ruin and we investigate their asymptotic efficiency. One, based upon a conditional Monte Carlo idea involving the order statistics, is shown to be asymptotically efficient in a certain sense. We use the simulation methods to study the accuracy of the standard Embrechts-Veraverbeke [16] approximation for the ruin probability and also suggest a new one based upon ideas of Hogan [21].

scholarly journals SIMPLE CONTINUITY INEQUALITIES FOR RUIN PROBABILITY IN THE CLASSICAL RISK MODEL

2016 ◽  
Vol 46 (3) ◽  
pp. 801-814 ◽  
Author(s):  
Evgueni Gordienko ◽  
Patricia Vázquez-Ortega
Keyword(s):  
Integral Equations ◽  
Ruin Probability ◽  
Simple Technique ◽  
Risk Model ◽  
Distribution Functions ◽  
Ruin Probabilities ◽  
Classical Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
The Classical Risk Model

AbstractA simple technique for continuity estimation for ruin probability in the compound Poisson risk model is proposed. The approach is based on the contractive properties of operators involved in the integral equations for the ruin probabilities. The corresponding continuity inequalities are expressed in terms of the Kantorovich and weighted Kantorovich distances between distribution functions of claims. Both general and light-tailed distributions are considered.

scholarly journals Nonparametric Estimation of the Ruin Probability in the Classical Compound Poisson Risk Model

2020 ◽  
Vol 13 (12) ◽  
pp. 298
Author(s):  
Yuan Gao ◽  
Lingju Chen ◽  
Jiancheng Jiang ◽  
Honglong You
Keyword(s):  
Nonparametric Estimation ◽  
Ruin Probability ◽  
Risk Model ◽  
Estimation Method ◽  
Asymptotic Distributions ◽  
Classical Risk Model ◽  
Compound Poisson Risk Model ◽  
The Fourier Transform ◽  
The Classical Risk Model ◽  
Asymptotic Variances

In this paper we study estimating ruin probability which is an important problem in insurance. Our work is developed upon the existing nonparametric estimation method for the ruin probability in the classical risk model, which employs the Fourier transform but requires smoothing on the density of the sizes of claims. We propose a nonparametric estimation approach which does not involve smoothing and thus is free of the bandwidth choice. Compared with the Fourier-transformation-based estimators, our estimators have simpler forms and thus are easier to calculate. We establish asymptotic distributions of our estimators, which allows us to consistently estimate the asymptotic variances of our estimators with the plug-in principle and enables interval estimates of the ruin probability.

scholarly journals The Distribution of the time to Ruin in the Classical Risk Model

2002 ◽  
Vol 32 (2) ◽  
pp. 299-313 ◽  
Author(s):  
David C.M. Dickson ◽  
Howard R. Waters
Keyword(s):  
Finite Time ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Classical Risk Model ◽  
The Classical Risk Model

AbstractWe study the distribution of the time to ruin in the classical risk model. We consider some methods of calculating this distribution, in particular by using algorithms to calculate finite time ruin probabilities. We also discuss calculation of the moments of this distribution.

scholarly journals SIMPLE CONTINUITY INEQUALITIES FOR RUIN PROBABILITY IN THE CLASSICAL RISK MODEL-CORRIGENDUM

2016 ◽  
Vol 47 (1) ◽  
pp. 359-359
Author(s):  
Evgueni Gordienko ◽  
Patricia Vázquez-Ortega
Keyword(s):  
Markov Chains ◽  
Ruin Probability ◽  
Risk Model ◽  
Applied Probability ◽  
Classical Risk Model ◽  
The Classical Risk Model

In Gordienko and Vázquez-Ortega (2016) page 801, the following reference was listed incorrectly: Yu, M.A. (2005) Sensitivity and convergence of uniformly ergodic Markov chains. Journal of Applied Probabilities, 42, 1003–1014. It should have instead been listed as: Mitrophanov, A. Yu. (2005) Sensitivity and convergence of uniformly ergodic Markov chains. Journal of Applied Probability, 42, 1003–1014.We sincerely regret the error and any problems that have resulted for the authors and readers.

Approximation of the Ultimate Ruin Probability in the Classical Risk Model Using Erlang Mixtures

2016 ◽  
Vol 19 (3) ◽  
pp. 775-798 ◽  
Author(s):  
David J. Santana ◽  
Juan González-Hernández ◽  
Luis Rincón
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Classical Risk Model ◽  
The Classical Risk Model
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